Code
# Download ZHVI data
zhvi <- read.csv("https://github.com/opengeos/datasets/releases/download/us/zillow_home_value_index_by_county.csv")Zillow Home Value Index Analysis with PDFM Embeddings
Comparing Linear, Ridge, and Lasso Regression Models
Introduction
This document demonstrates the application of Population Dynamics Foundation Model (PDFM) embeddings to predict Zillow Home Value Index (ZHVI) data. PDFM embeddings are 330-dimensional vector representations that capture complex spatial and demographic patterns.
Objectives
- Load and visualize Zillow Home Value Index data with geospatial mapping
- Join PDFM embeddings with home value data
- Build regression models to predict home values:
- Linear Regression (baseline)
- Ridge Regression (L2 regularization)
- Lasso Regression (L1 regularization with feature selection)
- Evaluate and visualize model performance
Why Ridge and Lasso Regression?
Ridge and Lasso regression are particularly useful when working with high-dimensional embeddings (330 features) because they:
- Ridge Regression (L2):
- Penalizes large coefficients to prevent overfitting
- Keeps all features but shrinks their impact
- Performs well when many features contribute to the outcome
- Lasso Regression (L1):
- Performs automatic feature selection by shrinking some coefficients to zero
- Identifies the most important embedding dimensions
- Produces sparse models that are easier to interpret
- Both:
- Use cross-validation to optimize the regularization parameter (lambda)
- More computationally efficient than stepwise regression
- Provide better generalization on unseen data
Setup and Data Loading
Load Required Libraries
Download Zillow Home Value Index Data
Load and Prepare ZHVI Data
Code
# constuct correct State FIPS code and Municipal FIPS code with leading zeros
zhvi_df <- zhvi %>%
mutate(
StateCodeFIP = str_pad(as.character(StateCodeFIPS), width = 2, side = "left", pad = "0"),
MunicipalCodeFIP = str_pad(as.character(MunicipalCodeFIPS), width = 3, side = "left", pad = "0")
)
# Create place identifier
zhvi_df <- zhvi_df %>%
mutate(
place = paste0("geoId/", StateCodeFIP, MunicipalCodeFIP)
)Note: The place column creates a unique identifier for each county by combining state and municipal FIPS codes, which will be used to join with geospatial and embedding data.
Geospatial Data Integration
Load County Geometries
Code
county_gdf <- st_read("https://github.com/zyang91/Google-Embedding-tutorial/releases/download/v2.0.0/county.geojson",quiet=TRUE)
couty_gdf <- county_gdf %>%
dplyr::select(place)Join ZHVI with County Geometries
Code
zhvi_county_gdf<- county_gdf %>%
inner_join(
zhvi_df,
by = c("place" = "place")
)Visualizing Home Values
Prepare Data for Visualization
Code
# Select specific date column for visualization
target_date <- "X2024.10.31"
viz_gdf <- zhvi_county_gdf %>%
dplyr::select(RegionName, State, all_of(target_date), geometry)Create 2D Choropleth Map
Code
# Create interactive map with Leaflet
pal <- colorNumeric(
palette = "Blues",
domain = viz_gdf[[target_date]],
na.color = "transparent"
)
leaflet(viz_gdf) %>%
addTiles() %>%
addPolygons(
fillColor = ~pal(get(target_date)),
fillOpacity = 0.7,
color = "white",
weight = 1,
popup = ~paste0(
"<strong>", RegionName, ", ", State, "</strong><br>",
"Home Value: $", format(get(target_date), big.mark = ",")
)
) %>%
addLegend(
position = "bottomright",
pal = pal,
values = ~get(target_date),
title = "Zillow Home Median Value",
opacity = 1
)